2. Concept of microstructural characterization
Why we need characterization ?
process
structure
property
performance
cause-and-effect target-and-means
Modern high performance steels
Performance Property Structure Process
austempering
Intercritical
annealing
Si or Al addition
Characterization in MSE
• What are the Items to be characterized?
– A material may have
• DIFFERENT PROPERTIES depending on THE STATE.
– The items should represent
• no other but THE STATE of the material.
– These items are what should be characterized.
• The items which describe THE STATE are;
– Composition
– Structure
– Morphology
• Composition
– Elemental: Major, Minor, Trace (Impurity),
– Elemental Distribution

• Volume, Thermal Stability, etc.
– Internal stress, Nature of stress and distribution
– Phase Stability
General procedure
Probe source
Input to specimen
Signal-matter interaction
Data collection and
processing
Interpretation
• Matter Wave
– Acoustic, Ultra-sonic
• Electromagnetic (EM) Wave
– RF, IR, Visible, UV, X-ray, gamma-
ray
• Elastic scattering
– XRD spectra, TEM contrast image
• Inelastic scattering
– SE image in SEM, EELS
• 2D / 3D Image
– Microscopy
• Microanalysis
– Spectrum
• Diffraction
– Spectrum or pattern
Consideration in characterization
• Select only the items necessary
– Fit to the purpose of the research
– Not the every item and not the every detail should be characterized
– What characterization techniques to use? The items and the detection
limit (resolution, accuracy, etc.)
• Precision
– Standard deviation of measured value
– An instrumental and human error
• Accuracy
– Deviation from the true value
– Mostly human error
• Mostly we are NOT short of number and distribution of instruments, BUT of
personal earnestness to use it.
• Mostly we are just throwing our problem to instruments, the “black box”,
without understanding the principle/theory, and thinking/planning the
experiment.
• Dangerous is just looking at an convenient and expensive instrument.
Science is NOT a routine job, BUT is an ADVENTURE to find/develop new
technique/knowledge
• A big and sophisticate instrument is a money sink with loss of versatility. The
order of detection limit and precision goes with the order of price, time, and
human salary.

• Cubic F + Cu at each lattice point = crystal of Cu
• Cubic F + C at 0,0,0 and ¼, ¼, ¼ = crystal of diamond
single or group of atoms
assigned to lattice point
lattice points Motif (Cu at 0,0,0 and Zn at ½, ½, ½)
• Cubic P + Cu at 0,0,0 and Zn at ½, ½, ½ = crystal of brass
Space group
• Combination of atomic arrangement around lattice points in 14
Bravais lattices  230 space group
• It provides criteria for filling the Bravais lattice point with groups
of atom
Crystallographic direction and plane
<u v w> : set of directions having equivalent properties
• Do not take reciprocal
• Always start from the origin
• Put direction in [ ] or in < >
for family of direction
{h k l} : set of planes having equivalent properties
Crystallographic direction and plane
Miller indices are written as [hkil] or (hkil) where, in all cases, the index i
is derived from h and k according to i = -(h+k) . Since the third index i
is not independent of the h and k, it is sometimes even omitted, and the
indices appear as [hk•l].
a1
a2
a3
a1
a2
a3
P
0,0,0
Miller-Bravais
Unit Cell
Miller Unit Cell
Miller:
[110] equals
Miller-Bravais
[1120]
Crystallographic direction and plane
Pyramidal plane (1
st
)
Prism plane (1
st
)
Basal plane
Prism plane (2
nd
)
Crystallographic direction and plane
Stereographic projections
• 2 dimensional presentation of crystallographic plane and direction
* The shortest distance between two points
on a sphere is along the great circle passing
through those points
Wulff net
• Angle between two arbitrary poles can be measured by rotating
the Wulff net until they lie on a great circle
Stereographic projections
• Stereographic projection in cubic system, where plane normal and
crystallographic direction with the same indices coincide

4. Diffraction analysis of crystal structure
Part 1
- Scattering and diffraction
- Conditions to observe diffraction in crystalline materials
(diffraction angle and intensity)
- Representation of diffraction in reciprocal lattice
Scattering of incident radiation
• Incident beam (X-ray, electron, neutron) interacts with matter
(electron or nuclei) to make scattered radiation
Scattering and diffraction
• Scattering implies interacting of incident beam with atom (radiating to all direction)
• When matter has a periodic array of atom, the arranged atom scattered the incident beam
in a specific direction, as we observe the intensity of scattered radiation as a function of
scattered angle (that is why we can use diffraction analysis to examine crystal structure)
Incident beam for diffraction
• The wave length of incident beam should be less than interatomic
spacing of lattice
• Possible candidates for incident beam : X-ray, electron, neutron
• Neutron
- Interaction with nuclei  improved efficiency for light atoms
- Usually penetrating sample
• X-ray
- Interaction with electron  good results for atoms with higher Z
- Diffraction occurs in sub-millimeter surface
• Electron
- Diffraction data is limited to submicron
Diffraction angle from crystal
• Scattered radiation from successive layer of
specific crystallographic plane (hkl) should
be in-phase
• If not, the scattered radiation will cancel out
to each other
Diffraction angle from crystal
θ1 θ1 θ1
x
1 2 1’ 2’
0 cos cos
1 1
= − θ θ x x
Bragg’s law
θ λ sin 2d n =
For cubic crystal:
2 2 2
l k h
a
d
hkl
+ +
=
( )
2 2 2
2
2
2
4
sin l k h
a
+ + =
λ
θ
• Bragg’s law is the minimum condition for diffraction
• This equation predicts, for a particular incident λ and a particular cubic crystal of
unit cell size a, all the possible Bragg angles at which diffraction can occur from
the plane (hkl).
• Diffraction directions are determined solely by the shape and size of the unit cell.
• All we can possibly determine about an unknown crystal by measurement of the
directions of diffracted beams are the shape and size of its unit cell.
• The intensities of diffracted beams are determined by the positions of the atoms
within the unit cell.
Intensity of diffraction
Bragg’s law condition
Structure factor Atomic scattering factor
Diffraction intensity from specific crystallographic plane
• We cannot observe the diffraction peak at all possible angle given by
Bragg’s law
• Atomic scattering factor results from the position of electron in an atom
• Structure factor is led by specific position of atom in the lattice structure
• And others...
Etc…
Atomic scattering factor
• Will the scattering intensity from an atom be the sum of scattering
intensity from all electron belonging to it ?
• Scattered radiation in wave front XX’ will be in phase, however, it is
out of phase at wave front YY’
 interference will decrease the intensity along this direction
Structure factor
• When atoms locate in corner of unit cell (ex. simple cubic structure), Bragg’s law
successfully predicts the angles where the diffraction occurs
• However, extra atoms exist (ex. body-centered position, face-centered position in
cubic lattice), it will affect the intensity of diffracted beam
• Out of phase when n=1 due to the scattering from body-centered
atom: (100) in BCC does not appear
• In phase when n=1 even with the scattering from body-centered
atom: (200) in BCC will appear
(n=1)
Structure factor
• FCC structure
- Extra atoms on plane parallel to (100), (110), (210), (211), …
• BCC structure
- Extra atoms on plane parallel to (100), (111), (210), …
Possible Forbidden
Simple cubic All None
Based centered h and k unmixed h and k mixed
Body centered (h+k+l) even (h+k+l) odd
Face centered h, k, l unmixed h, k, l mixed
Structure factor
• Plane with mixed ion : (200), (220) …  in phase interference
• Alternating plane with different ion : (111) …  in phase for even order diffraction
 out of phase for odd order diffraction
• Increasing or decreasing of diffraction intensity occurs
Structure factor
(100)
(110)
(200) reflection : 2
nd
order (100) reflection, usually not reflection from (200) plane
primitive BCC FCC
Reciprocal space and diffraction
• Reciprocal lattice : imaginary lattice where the direction of vector from origin to
(hkl) lattice point represent the plane normal of (hkl) plane in real lattice and the
magnitude is a reciprocal of plane spacing, 1/d
hkl
• From Bragg’s law, (1/d
hkl
) falls in the range of 0 ~ (2/λ), which constructs a limiting
sphere
• When we overlap this with reciprocal lattice, the reciprocal lattice points in the limiting
sphere have a potential to diffract the incident beam with wavelength λ

• In the direction of the incident beam, all the electrons in the atom will scatter in phase:
f(0) = Z. For θ > 0, f(θ) < Z, since at larger scattering angles the electrons around an
atom will scatter increasingly out of phase
• At a fixed value of θ, f will be smaller the shorter wave, since the path differences will
be larger relative to the λ, leading to greater interference between the scattered
beam

- However, some manufacturing process generates quite aligned crystallographic
orientation which is called as texture or preferred orientation

- Development of preferred orientation can change the relative peak intensity or even
make certain peak invisible
Random orientation
Strong texture
Distortion in diffraction intensity
• Residual stress
- Residual stress can affect the peak position and
relative intensity

- Macrostrress
: large number of neighboring crystals of the same
phase experience similar stress level
: displacement of the diffraction maxima from the
original position

- Microstress
: the stresses in the individual grains is widely
different and of opposite sign, while the average
stress sums to zero
: peak broadening

- Peak shift or broadening can be used to determine
the residual stress level in the sample
However, the measurement is confined to surface
layer
Distortion in diffraction intensity
• Crystalline size
- Smaller the crystalline size makes the diffraction
peak to be widened

- It comes from incomplete destructive interference
of diffracted beam

- The incident X-ray beam is not perfectly parallel and
it includes a range of incident angle from θ
1
~ θ
2

10 eV 50 eV
5 eV
Energy of incident electron
Resolution of signals
• Resolution in an SEM is
ultimately determined by
the size of the region from
which signal is produced.
Thus, for the same region
of excitation the resolution
from the three signals
differs and decreases from
secondary to backscatter
to X-rays.
• Factors affecting size of the interaction region:
- Diameter of the primary beam
- Energy of the primary beam
- Atomic weight of the specimen
- Coating of specimen
Resolution of signals
BSE
SE
Image contrast from BSE
light element heavy element
• No significant difference in secondary
electron coefficient depending on Z

• Back-scattered electron coefficient
increases with increasing Z
• Fraction of back-scattered electron
as a function of the average atomic
number
• BSE image of polished surface
Nb-rich intermetallic
compound (heavy)
Alumina matrix
(light)
• Crystallographic (or channeling) contrast of BSE
- The plane orientation affects the penetration of the electron beam into the
crystal because the atomic packing density varies with crystallographic plane.
- The BSE coefficient (η) is dependent on the orientation of crystallographic
planes with respect to the direction of the electron beam (For higher penetration,
the η is lower).
Electron channeling contrast
BSE detector in SEM
Image contrast from SE
• Contrast effects in S.E. image are due to surface topography, or more precisely,
to the local curvature of the surface.
• Changes in local curvature change the probability that a S.E. generated near the
surface can escape. Edges look bright, flat surfaces look dull.
Fracture surface of polycrystalline alumina
r : distance needed to escape from sample
L
s
: mean free path of secondary electron
Image contrast from SE
• Location of ET detector leads to shadowing
• Increasing the detector bias will wash out the shadows.
• Previous image turned upside down.
• We need to know where the detector
is to tell bumps from pits!
Positive voltage
Trajectory effect
S.E. B.S.E.
Resolution nm’s ~10
2
nm
Energy eV’s (<50 eV) ~E
0
(0.8E
0
)

• Gas-assisted etching
: reactive gases are delivered to the sample
surface by needle
: interaction of ion beam with the gas causes
formation of evaporable volatile species
which are pumped away by vacuum system

• Gas deposition
: metallorganic gases are delivered to the
sample surface by needle
: dissociation of gas molecules on the exposure
to the ion beam
: deposition of the metallic atom and removal of
organic ligands

• Maximum wavelength of characteristic X-ray
being diffracted is about 1.9d

• Longer wavelength (lighter element) requires
analyzing crystal with larger plane spacing
n
d θ
λ
sin 2
=
WDS spectrum
• Ni-base super alloy (a) LiF crystal and (b) TAP crystal
• Combinatory use of analyzing crystal is required to scan wide range of wavelength.
• Although an analyzing crystal with small d-spacing limits the range of detectable atomic
numbers, the small d-spacing can increase angular dispersion which provides higher
resolution.
θ λ
θ
cos 2d
n
d
d
=
Energy dispersive spectroscopy
• Detector collects the signals of characteristic X-ray energies from a whole range of
elements in a specimen at the same time.
• EDS system does not have moving part such as rotating detector, so it is structurally
simple.
• Typical resolution of EDS is ~140 eV that is worse than WDS ( ~10 eV)
• Lightest element that can be detected is O (Z=8), not C (Z=6)
• Low cost and fast analysis
Detector in EDS system
• Si detector is commonly used.
• The average energy of photon needed to
generate an electron-hole pair is ~3.8 eV
in Si diode
• The higher photon energy comes, the more
pairs are generated.
• The characteristic X-ray photon is separated
by their energy levels according to the number
of electron-hole pairs they generate.
2 2
)] ( 35 . 2 [ FE e R
i noise
+ = σ
- Electronic noise which is strongly
dependent on temperature.
- Detector usually operates at the
temperature of liquid nitrogen.
EDS spectrum
• EDS is a standard part of modern SEM and TEM.
• The reason to use EDS rather then WDS is compactness.
• EDS in electron microscopy uses high energy electron beam as a source to excite
characteristic X-ray.
• EDS in electron microscopy is useful for analyzing the chemical elements in microscopic
volume because the electron beam can be focused on a very small area (microanalysis).
Emission volume
3 gram/cm
3
10 gram/cm
3
• The characteristic X-ray are excited from a volume under the surface of the specimen,
not from an area on the surface.

• In particular, EDS analysis using SEM, the EDS signal are emitted from a lateral area
that is much larger than the probe diameter.

• To obtain a better spatial resolution, we should choose an accelerating voltage that is not
much higher than that necessary to excite the required characteristic X-ray.
X-ray production regions with different mass
densities.
Emission volume
• For thin specimen as used in TEM, the spatial resolution is of less concern.

δE = Electron energy loss
(contribute to a background)
• We are measuring Secondary Electrons emitted
from the surface in XPS.
• The secondary electrons which are emitted are
only from the near surface region of the
specimen, due to the limited mean free path of
the secondary electrons.
• For most materials the XPS measurement is
limited to 2-5 atomic layers at the surface.
Equipment
XPS
AES
X-ray sources for XPS
• Mg Kα and Al Kα exhibit line widths less than 1.0 eV and also have sufficient energy (>1000 eV)
for photoelectron emission
XPS spectrums
1. Photoemission from core electron levels
2. Auger emission excited by X-rays
3. Photoemission from valence levels
4. A step-like background (increasing with binding energy)
E
K
= hν – (E
B
+ φ)
Background:
Photoelectrons with
energy loss, δE
Peak:
Photoelectrons without
energy loss
E
K
shift by 233 eV when we change the radiation from Al Kα to Mg Kα
XPS peak identification
E
B
= hν – (E
K
+ φ)
Chemical shift in XPS
Chemical shift: Change in binding energy of a core electron of an element
due to a change in the chemical bonding of that element.
Withdrawal of valence electron charge increase in binding energy
(oxidation)
Addition of valence electron charge decrease in binding energy
Qualitative view:
Core binding energies are determined by:
Electrostatic interaction between it and the
nucleus, and reduced by:
• Electrostatic shielding of the nuclear charge
from all other electrons in the atom (including
valence electrons)
• Removal or addition of electronic charge as a
result of changes in bonding will alter the
shielding
Chemical shift in XPS
Binding energy of 1s electron in carbon increases
with being bonded to more electronegative atom
• XPS peaks give additional information on the chemical bonding state of material.
For example, oxidation states of metals
AES spectrums
• Differential mode is more widely used because
the Auger peaks are more obvious than direct mode
• Principal Auger KLL peaks of light elements.
• The Auger signal is sensitive to changes in
chemical bonds, which result in shifts of the
main peak, and a change in shape of minor
peaks.
• Chemical shift in AES is significantly larger than
the shift in XPS but more difficult to interpret.
AES peak identification
AES element imaging
Auger electrons are a type of secondary electrons, so like XPS, this is
a near surface technique.
Spatial Resolution:
Defined by the beam size and the
backscattered electron volume
• Diameter of electron beam can be as small as
about 10 nm when a FE-gun is used.
• Focusing of X-ray beam is difficult because it is
electrically neutral and can not be focused with
electromagnetic field.
Depth profiling
Calibration of depth scale:
• Sputtering rate determined from the time required to sputter through a
layer of the same material of known thickness.
• After the sputtering analysis, the crater depth is measured using depth
profilometer. A constant sputtering rate is assumed.
Depth profiling of oxidation layer
Steel substrate
Al oxides line
MnO layer
Dew point -10℃
Al oxide layer
Dew point -30℃

9. Secondary ion mass spectroscopy
3-Dimensional atom probe tomography
- Principles and application of SIMS and 3DAP
Surface analysis by SIMS
We have used sputtering to obtain a depth-profile in XPS and Auger. Why not measure the
ions we remove during sputtering, rather than a photon or electron?
Ar
+
, Ga
+
, Cs
+
,
O
2
+
, Xe
+
(E = 1 - 20 keV)
Neutrals
Secondary Ions
SE’s
• The majority of the secondary particles
are neutral, only ~1% of total secondary
particles are ionized.
• Secondary ions go into an analyzer
where we measure the mass-to-
charge ratio, which is used to identify
the type of ion.
• More than one-to-one knock-out of a
surface ion but a series of collisions
(collision cascade)
Interaction with ion beam
a) Direct collision of sputtering is extremely
fast, occurs in the range of 10
-15
-10
-14
s after
the primary ion strikes the surface.
b) Indirect collision (Collision cascade):
The primary ions induce a series of collision.
Atoms in the solid transfer impact energy to
surface atoms after a series of collisions
(10
-14
-10
-12
s)
c) Thermal collision (transient vaporization)
occurs when the density of ions is high.
(10
-13
-10
-10
s)
Advantage of SIMS
Advantages of SIMS over electron spectroscopy:
• Detection of all chemical elements (H-U) in the periodic table, including hydrogen
which cannot be detected by the AES and XPS (because of poor core level definition)
;
• Detection of elements in concentration as low as 10
-9
(ppb detection limit), while AES
and XPS detection limits are concentration levels of 0.1 atom%;
• Limitation of the detection to the top one or two atomic layers of a solid surface (<
1 nm); and
• Distinguish between different isotopes of elements.
• Large dynamic range
Disadvantages:
• Destructive
• Complexity of ion yield(difficulties in quantitative analysis)
Signal intensity of secondary ion
η θ α
m m p m
Y I I
+
=
I
p
: Primary ion flux
Y
m
: Sputtering yield
α
+
: Probability for positive ions
θ
m
: Fractional concentration of
species m in the surface layer
η: Transmission of detector system
(ion detected / ion emitted = 0 ~ 1)
• A sputtered particle faces competition between ionization and neutralization processes
when it escapes a sample surface.
• Ionization probability represents the chance of a sputtered particle being an ion.
Positive ion yield under bombardment of 13.5 keV O
-1
Signal intensity of secondary ion
• Ionization probability is strongly affected by the electronic properties of the sample matrix.
• I
m
<< I
oxide
• Significant variation in secondary ion yield with chemical elements and chemical states of
the surface, which makes quantitative analysis difficult.
In most cases the yield of singly ionized atom
s predominates.
Static and dynamic SIMS
• Sputtering is, fundamentally, a process damaging a surface
• Therefore, the chemical structure of the surface may be destroyed during SIMS
measurement

\
|
=
−
z
m
V L t
• The m/z (mass to charge) of ions is analyzed by measuring their flight time in the analyzer.
• Heavier ions will have longer flight times in the tube.
• To measure the time of flight, precisely pulsed primary ions should be used (pulse period ~
10 ns).
• The ions are reflected by a mirror.
• The mirror is composed of a series of precisely spaced rings to which a gradually increasing
electric field is applied.
• Ions with higher kinetic energy will penetrate further into the mirror before being reflected.